Article1979

The Effect of Long Term Dependence on Risk-Return Models of Common Stocks

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Financial Markets and Investment Strategies Financial Risk and Volatility Modeling Complex Systems and Time Series Analysis

Abstract

In a previous paper the authors have shown that common stock returns are characterized by a phenomenon called long term dependence. The present paper discusses the implications of the presence of long term dependence for existing risk-return models in finance. Specifically, it is shown that (1) risk rankings of stocks or portfolios tend to vary with the differencing interval chosen to measure security returns, (2) efficient portfolios vary with the differencing interval selected, and (3) the unrealistic, homogeneous time horizon assumption of the capital asset pricing model must be retained in order for the model to hold.

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1964CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK*1970EFFICIENT CAPITAL MARKETS: A REVIEW OF THEORY AND EMPIRICAL WORK*1968Fractional Brownian Motions, Fractional Noises and Applications 1975THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCK PORTFOLIOS AND CAPITAL BUDGETS**This paper is another in a series of interrelated theoretical and statistical studies of corporate financial and investment policies being made under grants from the Rockefeller Foundation, and more recently the Ford Foundation, to the Harvard Business School. The generous support for this work is most gratefully acknowledged. The author is also much indebted to his colleagues Professors Bishop, Christenson, Kahr, Raiffa, and (especially) Schlaifer, for extensive discussion and commentary on an earlier draft of this paper; but responsibility for any errors or imperfections remains strictly his own.[Professor Sharpe's paper, “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk” (Journal of Finance, September 1964) appeared after this paper was in final form and on its way to the printers. My first section, which parallels the first half of his paper (with corresponding conclusions), sets the algebraic framework for sections II, III and VI, (which have no counterpart in his paper) and for section IV on the equilibrium prices of risk assets, concerning which our results differ significantly for reasons which will be explored elsewhere. Sharpe does not take up the capital budgeting problem developed in section V below.]1959Portfolio Selection: Efficient Diversification of Investments 1966Equilibrium in a Capital Asset Market 1968THE PERFORMANCE OF MUTUAL FUNDS IN THE PERIOD 1945–1964 1963A Simplified Model for Portfolio Analysis

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